r^2+2r-85=-3

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Solution for r^2+2r-85=-3 equation:


Simplifying
r2 + 2r + -85 = -3

Reorder the terms:
-85 + 2r + r2 = -3

Solving
-85 + 2r + r2 = -3

Solving for variable 'r'.

Reorder the terms:
-85 + 3 + 2r + r2 = -3 + 3

Combine like terms: -85 + 3 = -82
-82 + 2r + r2 = -3 + 3

Combine like terms: -3 + 3 = 0
-82 + 2r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '82' to each side of the equation.
-82 + 2r + 82 + r2 = 0 + 82

Reorder the terms:
-82 + 82 + 2r + r2 = 0 + 82

Combine like terms: -82 + 82 = 0
0 + 2r + r2 = 0 + 82
2r + r2 = 0 + 82

Combine like terms: 0 + 82 = 82
2r + r2 = 82

The r term is 2r.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2r + 1 + r2 = 82 + 1

Reorder the terms:
1 + 2r + r2 = 82 + 1

Combine like terms: 82 + 1 = 83
1 + 2r + r2 = 83

Factor a perfect square on the left side:
(r + 1)(r + 1) = 83

Calculate the square root of the right side: 9.110433579

Break this problem into two subproblems by setting 
(r + 1) equal to 9.110433579 and -9.110433579.

Subproblem 1

r + 1 = 9.110433579 Simplifying r + 1 = 9.110433579 Reorder the terms: 1 + r = 9.110433579 Solving 1 + r = 9.110433579 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = 9.110433579 + -1 Combine like terms: 1 + -1 = 0 0 + r = 9.110433579 + -1 r = 9.110433579 + -1 Combine like terms: 9.110433579 + -1 = 8.110433579 r = 8.110433579 Simplifying r = 8.110433579

Subproblem 2

r + 1 = -9.110433579 Simplifying r + 1 = -9.110433579 Reorder the terms: 1 + r = -9.110433579 Solving 1 + r = -9.110433579 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + r = -9.110433579 + -1 Combine like terms: 1 + -1 = 0 0 + r = -9.110433579 + -1 r = -9.110433579 + -1 Combine like terms: -9.110433579 + -1 = -10.110433579 r = -10.110433579 Simplifying r = -10.110433579

Solution

The solution to the problem is based on the solutions from the subproblems. r = {8.110433579, -10.110433579}

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